LYNCHBURG, Va. - The second act of the immigration debate is starting as a sharp reality check on the first, with House leaders bluntly declaring that they have no intention of being influenced by the Senate's strong support of the bill last week.

"We shouldn't feel pressured by the Senate, the president or anyone else," Rep. Bob Goodlatte, chairman of the Judiciary Committee, told an audience at a town meeting here Tuesday night. "Getting it right is more important than passing a bill."

His sentiment drew booming applause from a crowd at the Lynchburg Public Library, where objections to the sweeping overhaul of the nation's immigration system were voiced loudly. He listened as several voters rose from their seats, smiling when one man said: "This immigration bill stinks to high heaven!"

While the Senate spent most of June making its case on the immigration bill, the month of July belongs to the House, where the debate will start taking shape next week. It is already unfolding as a rebuttal to the Senate, making clear the outcome of the immigration measure is deeply uncertain.

"The Senate bill, in my opinion, repeats the mistakes made by the Congress in 1986," Goodlatte said. "It gives 11 million people a legal status almost immediately."

The path to citizenship is a pillar of the Senate bill, which passed with 68 votes, including all Democrats and 14 Republicans. But it is a deal breaker to many in the House, a point that Goodlatte said was non-negotiable to his Republican colleagues when they meet next Wednesday to plan a way forward on the immigration debate.

Goodlatte, who was elected to Congress in 1992 from a district that covers a wide swath of western Virginia, raised questions about the component of the Senate bill that would double border patrol agents. The plan was a key enticement to many GOP senators, but Goodlatte said it overlooked the need for border agents in the "interior of our country," where many undocumented immigrants live.

On a rainy evening, more than 100 people turned out to hear Goodlatte and ask questions about the IRS controversy, the investigation into the attack on the U.S. consulate in Benghazi, Libya, and the NSA surveillance programs. He and other members of Congress are spending the week taking the pulse of their constituents during a week-long break from Washington.

But it was immigration that drew the most intense exchange here in Lynchburg, particularly as the 90-minute town meeting drew to a close and the congressman called on a young woman seated near the front.

Dulce Elias, a 16-year-old junior at Harrisonburg High School, said she had been living in the United States since the age of 3 and worried that she and her parents would be deported. She said they are undocumented immigrants - two of the estimated 11 million living and working in the U.S.

As she told her story, she began to cry. The congressman listened patiently throughout and thanked her for having the courage to attend the meeting and speak.

"Someone who was brought here by someone else at age 3 has not done anything wrong and I want you to know that," Goodlatte said, standing a few feet from the young woman. "As part of solving this overall problem, people like you should be addressed. But I do think we have to do it differently than the Senate did."

After the meeting, Elias waited in line to shake Goodlatte's hand and asked him for a hug. He smiled as he wrapped his arms around her.

He told ABC News that her story - like scores of others he has heard from immigrants - was compelling. But he said laws cannot be written based on emotion alone, adding that enforcement must be stepped up for people who came to the U.S. illegally as well as new laws written for legal immigration reform.

When one man suggested that House Republicans were trying to delay the immigration legislation, Goodlatte responded with vigor.